MATLAB Code Implementation for Curve Fitting

Curve fitting is a highly practical function in MATLAB, primarily used to find mathematical functions that best describe data trends. Through fitting, we can extract continuous functional relationships from discrete data points, which is significant for data analysis and prediction.

In MATLAB, the most common method for implementing curve fitting is the least squares approach. This method finds optimal fitting parameters by minimizing the sum of squared vertical distances between data points and the fitted curve. For linear relationships, we can use polynomial regression; for more complex nonlinear relationships, we may need to use exponential, logarithmic, or other custom function forms.

MATLAB provides built-in functions such as polyfit and polyval for polynomial fitting. The polyfit function calculates fitting coefficients using the least squares algorithm, taking input arguments of x-data, y-data, and polynomial degree. The polyval function then generates points on the fitted curve using these coefficients with syntax polyval(p,x) where p represents the polynomial coefficients. Users can quickly obtain fitting results by simply providing the x,y coordinates of data points and the desired polynomial degree.

Beyond polynomial fitting, MATLAB also supports various nonlinear fitting methods. Through functions in the Optimization Toolbox, such as lsqcurvefit or fit (from Curve Fitting Toolbox), users can implement more complex curve fitting models. When performing fitting, selecting appropriate models and degrees is crucial - excessively high degrees may lead to overfitting, while insufficient degrees may result in underfitting. Model selection can be validated using metrics like R-squared or RMSE.

A robust curve fitting program typically includes data visualization capabilities, allowing users to visually compare raw data and fitting results. MATLAB's powerful plotting functions, such as plot() for curves and scatter() for data points, make this easy to implement. By creating scatter plots of original data and overlay fitting curves, we can quickly assess fitting quality and validate the model's effectiveness through residual analysis.